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Target Tracking for UWB Multistatic Radar Sensor Networks Bita Sobhani, Student Member, IEEE, Enrico Paolini, Member, IEEE, Andrea Giorgetti, Senior Member, IEEE, Matteo Mazzotti, Member, IEEE, and Marco Chiani, Fellow, IEEE
Abstract—A multistatic radar based on ultra-wideband (UWB), also known as a UWB radar sensor network, has been shown to represent a very promising solution to localize an intruder moving within a small surveillance area. In this paper, a tracking algorithm based on low-complexity particle filtering is proposed, specifically tailored to UWB radar sensor networks with one transmitter and several receivers. An expression to calculate the particle weights is first derived, combining observations from all receivers. The particle filter is then modified to solve problems caused by blind zones inherently associated with the use of the UWB technology and multistatic configuration. In the proposed improved algorithm, suitable low-complexity particle filtering is employed to estimate velocity. The proposed approach provides high accuracy even at low signal-to-noise ratios with either static or dynamic clutters and it can track complicated maneuvering trajectories. Index Terms—Kalman filter, multistatic radar, particle filter, target tracking, ultra-wideband.
I. INTRODUCTION
P
RECISE localization and tracking of moving targets inside an area is of great interest for several surveillance applications. Localization is usually intended as the capability to locate friendly collaborative objects. This is sometimes referred to as active localization, because the object to be localized collaborates to its localization process [1]. However, an increasing attention is recently being devoted to the capability of detecting and tracking unfriendly non-cooperative objects within a given area. This is referred to as passive localization and is typical of radar systems [2]. In order to improve the localization performance of the system, tracking is an essential component to achieve high-level system reliability.
Manuscript received January 31, 2013; revised June 06, 2013 and September 30, 2013; accepted October 03, 2013. Date of publication October 22, 2013; date of current version January 15, 2014. This work was supported in part by the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement “CONCERTO” n. 288502 and in part by the Italian Ministry of Education, Universities and Research (MIUR) under Research Projects of Significant National Interest PRIN 2011 “GRETA” and PRIN 2009 no. 2009A85F98_003. The guest editor coordinating the review of this manuscript and approving it for publication was Dr. Richard Martin. B. Sobhani, E. Paolini, A. Giorgetti, and M. Chiani are with the Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi” (DEI), University of Bologna, 47521 Cesena, Italy, and also with CNIT, 47521, Cesena, Italy (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). M. Mazzotti is with the Center for Industrial Research on ICT (CIRI ICT), University of Bologna, 47521 Cesena, Italy, and also with CNIT, 47521, Cesena, Italy (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTSP.2013.2286771
Unlike a monostatic radar, a multistatic radar uses at least three non co-located antennas for transmitting and receiving [3]. The major advantages of a multistatic radar over a conventional monostatic one include a wider area coverage and a higher amount of information available due to spatial diversity. Moreover, receivers in a multistatic radar system are not required to transmit any signal, which enables development of low power and low cost equipment. These features lead to improved performance and foster new applications such as anti-intruder surveillance, ambient monitoring in safety and healthcare applications or location-aware commercial services. A promising wireless technique for such multistatic radar applications is the ultra-wideband (UWB) technology, especially in its impulse radio (IR) version. As it is characterized by the transmission of a few nanoseconds duration pulses [4], [5], IR UWB offers an extraordinary resolution and localization precision. Additional advantages include low power consumption, high spatial resolution (typically a few centimeters) even in indoor environments with dense multipath, high security and low probability to be intercepted, co-existence with a large number of devices operating in small areas, and robustness to narrowband jamming [6]. The above features and the fact that IR UWB devices are usually light-weight, cost-effective, and characterized by lowpower emissions, make UWB an ideal candidate for short-range radar sensor network applications [7]–[11]. The radar sensor networks addressed in this paper are UWB multistatic radar systems aimed at detecting and tracking non-cooperative targets (e.g., human subjects) moving inside a surveillance area. Passive localization through multistatic UWB radars is the subject of several works such as [12]–[17] a few of which, however, focus on tracking aspects. In this context, the measurement equation is non-linear and also the measurement noise cannot be assumed as Gaussian. Therefore, the commonly used tracking filters based on linearity and Gaussianity assumptions, such as the Kalman filter, are not expected to exhibit a satisfactory performance, even if they may still represent a valuable choice due to their low complexities [18]. Good candidates for UWB-based radar systems are non-linear Bayesian filtering algorithms such as particle filters [19], [20]. It is claimed in [21] that, while such Bayesian nonlinear filters constitute an optimal solution, their implementation is problematic due to their high computational complexity. A new tracking algorithm based on a threshold filter is then proposed. A related tracking approach was proposed in [22]. In [23], both Kalman and Bayesian filtering have been considered, in the framework of a pixel-based approach.
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Although exhibiting a good performance, this pixel-based approach has also some drawbacks. Firstly, it limits the position accuracy to the pixel size. Secondly, it entails high computational complexity and memory requirements. The complexity grows dramatically with the number of state dimensions, size of the area and number of targets. In [24], an algorithm based on particle filtering for UWB ranging and tracking is proposed. It demonstrates the advantages of particle filtering compared to conventional tracking methods. However, this algorithm is tailored for bistatic radars for small distance ranging. In this paper, a multistatic UWB radar based on one transmitter and multiple receivers is considered, employing particle filtering for target tracking. We assume a continuous state space, focusing only on particles wherein the target is more likely to be present. At each scan time, the particles are predicted according to a dynamic model and then evaluated by giving a weight to each of them based on the observations. The final estimated position is obtained as the weighted sum of all particles. In the process, we derive an expression for weights calculation based on observations from all receivers. Conventional particle filtering may lead to track divergence due to intrinsic peculiarities of UWB multistatic radars. Mainly, these divergences are caused by blind zones, i.e., regions inside which the target cannot be detected by at least one of the receivers. The blind zone problem also affects Kalman filtering, that may even lose the track if the target remains hidden long enough [25]. Around the blind zones where the observations are not reliable for a considerable number of scan times, any strong clutter residue, a target maneuver or an extremely low signal-tonoise ratio can corrupt the velocity estimation and cause a divergence. The tracking is also prone to be diverged in far areas from the transmitter and the receiver antenna, because UWB signals are highly attenuated by distance. To cope with the blind zone problem, we propose a lowcomplexity modified particle filter, to improve the velocity estimation. In particular, we calculate the average velocity over a sliding window. Within each window, we assign a weight to each estimated velocity according to its difference from the average velocity calculated in the previous scan time. The higher the difference, the lower its contribution to the mean. We also propose to increase the process noise standard deviation proportionally to this error to cover any potential maneuver. We show by numerical simulation that the proposed algorithm provides high estimation accuracy even at low signal-to-noise ratios in the presence of either static or dynamic clutter. Moreover, it can track complicated maneuvering target trajectories. A further advantage of our algorithm is that the tracking filter does not require the estimated target position as input. The detection and localization steps at every scan time can be skipped for a single target tracking except for the first and second scan times to initialize the track. Finally, we remark that the proposed algorithm based on particle filtering can be implemented for real-time tracking. The paper is organized as follows. In Section II, a system description is presented and equations for particle weights are derived. A tracking algorithm based on particle filtering with the derived weights is explained in Section III. In Section IV, a modified tracking algorithm is presented to solve divergence
Fig. 1. Pictorial representation of the UWB multistatic radar system considered in this paper.
problems caused by blind zones. In Section V, numerical results are illustrated and the performance of our proposed particle algorithms is compared to that of Kalman filtering in various scenarios. Conclusions are provided in Section VI. II. SYSTEM DESCRIPTION A. The UWB Multistatic Radar Setup We consider a UWB multistatic radar system composed of one transmitting (TX) node and receiving (RX) nodes. The transmitter and multiple receivers may, for example, be deployed on the perimeter of the area as it is depicted in Fig. 1. A central node collects the received signals from all of the receiver nodes and performs the tracking procedure. During a frame time of duration , a sequence of UWB pulses at intervals (the interpulse period) is emitted by the TX node, i.e., . The transmitted pulse at time is assumed to be the first derivative Gaussian monocycle (1) with duration parameter . The system is designed in such a way that the channel response to a single pulse when a moving target is present does not change appreciably during a frame time. If a target is present inside the area, the received signal at each RX node corresponding to a UWB transmitted pulse consists of the direct path pulse followed by pulse replicas due to both the clutter and the target and the additive noise [23]. B. The Blind Zone Problem One of the problems in UWB multistatic radar systems are blind zones for each pair of TX and RX antennas. Blind zones are consequence of two main concurrent phenomena. Firstly, this problem always arises in presence of a non-ideal synchronization. In the considered system, in fact, synchronization is the first task to be performed, based on time-of-arrival (ToA) estimation of the direct-path pulse. This operation is essential both to align the pulse responses belonging to the same frame in order to achieve a process gain and to align successive frames to perform clutter removal. Synchronization based on ToA estimation is never ideal, thus leading to an imperfect frame alignment. A residue of direct-path pulse is then
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detected by the system. To simplify the derivation of particle weights we consider that the received pulse from direct path and the clutter are removed completely.2 Therefore, the received waveform is3 (2) is the UWB reference pulse,4 is In the above equation, the delay of the pulse scattered by the target and is the additive white Gaussian noise. Note that channel gain is a real positive or negative value and we assume it to be constant over one frame.5 After sampling the received signal, we denote the vector of samples for each frame corresponding to the ’th receiver by , where: Fig. 2. Example of quantized ellipses in case of three receivers.
always present in real systems after clutter removal processing. The problem is that the direct path is usually much stronger than the target echo and the other clutter components, due to the fact that it does not experience reflections. Hence, the direct path residue after clutter removal typically masks the echo of a moving target that is close to the direct TX-RX path.1 Another issue concurring to the blind zone effect, even in presence of a perfect ToA estimation, is related to sampling resolution which maps the target position onto “quantized” ellipses inside the area. For example, denote the propagation delay times corresponding to target and direct path by and , respectively, where and are the target-RX and TX-target distances and is the TX-RX distance. Moreover, denote by the sampling period of the received signal, and by and the integers and , respectively. For we have and the target position is assumed on the direct TX-RX path, leading to a mismatch between the actual and the estimated value of . This position estimation error caused by finite sampling, which is present whatever the target position, is prominent in the proximity of the direct TX-RX path. Fig. 2 depicts “quantized” ellipses for each pair of TX and RX antennas that correspond to the points such that , where from the inner ellipse toward the outer one. For each TX-RX pair, all the points within the most inner ellipse are mapped onto the direct TX-RX path. C. Particle Weight Derivation We start by considering a single pair of transmit and receive antennas. Let us assume that is the received signal at the ’th receiver, obtained by averaging the received waveforms corresponding to the pulses transmitted within a frame. In particle filtering the particles are taken on the target state space [19]. We assume that the presence of target has already been 1The same signal masking effect may arise also when the moving target is not
close to the direct path, in case other reflectors with dominant radar-cross-sections are characterized by a similar TX-scatterer-RX delay. This issue, although not addressed in this paper, is a further element motivating the design of smart and robust tracking algorithms.
(3) , where stands for rounding toward the with closest integer and is the sampling period. In Bayesian tracking, we need to know the likelihood for the received vector and each of the particles from state space . The state space , as we define precisely later for each of our particle algorithms, may include target position components with or without target velocity components. If the target state space is known, it means that we know the corresponding delay of the target echo. According to (3), , , is known and we can estimate the amplitude by means of some estimation approach. For now, assume that we already have the estimation for . From (3) it can be seen that each is a Gaussian distributed random variable with mean equal to and variance equal to the received noise variance , that is, , . Given the statistical independence of noise samples we have: (4)
Note that in the above equation, is a function of . This dependency is not explicitly shown for the sake of simplicity. In this paper, we adopt the Maximum Likelihood (ML) approach for estimating the echo amplitude, i.e., we determine the which maximizes the likelihood function . After simple calculations, it turns out that the ML estimation for is (5) 2Nevertheless, the numerical results presented in Section V will account for non-ideal clutter removal to assess the performance of the proposed algorithm in a realistic setup. 3Since we consider UWB signals, equivalent baseband notation is not adopted and all signals are real. 4It is the transmitted pulse, but it may also include antenna and channel propagation distortions. 5The radar cross section of the target depends highly on its orientation and characteristics and also the frequency [26], [27]. However, considering complicated models makes mathematical derivations more complicated and introduces additional computational complexity.
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By replacing (5) in (4) we have:
(6)
We can see in the above equation that is equal to ’th sample of the vector obtained by cross-correlating the received vector with the reference pulse vector . Let us denote this cross-correlated re. Moreover, the expression ceived vector by in the above equation is in fact the energy of the reference pulse vector , that we denote by . We obtain (7) Fig. 3. Flowchart of the proposed tracking algorithm with particle filtering.
We now generalize the likelihood to the multistatic case with a single TX and RX antennas. Since the received vectors are statistically independent, we have
In the above equation, is the state transition matrix related to the scan time duration (frame duration) by:
(10) (8)
The likelihood is used to calculate the particle weights during target tracking. In this paper we consider Sampling Importance Resampling (SIR) particle filtering [19] in which resampling is done at each scan time. Therefore, the weight of particle at the ’th scan is only proportional to the likelihood and not dependent on its previous weight, where denotes the state of the ’th particle at the ’th scan. III. TRACKING ALGORITHM The flowchart of the proposed tracking algorithm is illustrated in Fig. 3. At every scan time (frame time), a central node collects the received vectors from all of the RX nodes and performs the tracking according to the following algorithm. Assume that we have particles. As shown in the figure, initial particles are taken from a normal distribution with mean equal to the estimated initial state and covariance matrix equal to the process noise covariance matrix (defined later), that is . Then in the time update step, particles are predicted according to the dynamic model assumed for the target. In this paper, we assume a straight-line constant-velocity motion model for the target according to:
Furthermore, is the process noise taken from a normal distribution with zero mean and covariance matrix equal to
(11)
where is the target acceleration noise variance [28]. Next, we need to calculate the likelihood function for each particle . For this purpose, we first calculate the delay of target echo with respect to each receive antenna . This can be obtained by the sum of the particle distances from the transmitter and the ’th receiver, , divided by the speed of and the coorlight . Indicating with dinates of the TX and ’th RX antenna, respectively, and with the ’th element of a generic vector , we have:
(12)
(9) is the target state at the ’th scan time. We assume that where the state is a 4 1 vector containing the position and velocity components in and directions, i.e., .
’th Then according to this delay which is equivalent to the sample, we compute the exponential function for the likelihood using (8). Next in weight update step, we normalize this likelihood over all particles and assign it to as the weight of
SOBHANI et al.: TARGET TRACKING FOR UWB MULTISTATIC RADAR SENSOR NETWORKS
particle . In order to avoid degeneracy problem of particle filters, systematic resampling is done at each scan time that replaces low probability particles with high probability particles, keeping the number of particles constant [19]. After the resampling step, all new particles will have the same weights equal to . Then, we calculate the estimated state by the weighted sum of all particles. Finally, the outputs are saved in a track file and the algorithm steps are repeated for the next scan of data.
and the target had a maneuver. Later, in Section V, we show that even without increasing the process noise standard deviation according to errors, the algorithm is able to track extremely complicated trajectories. However, we consider it as a part of our algorithm to add more robustness and flexibility. In fact, our modified algorithm uses a particle filter for estimating the velocity in which the particles are the estimated velocities within the window. We assume the following dynamic model for the target:
IV. MODIFIED TRACKING ALGORITHM The previous tracking algorithm is a conventional SIR particle filtering in which the weights are derived for UWB multistatic radar applications. Although this approach is algorithmically straightforward, it suffers from the problem of instability. The tracking process may diverge due to strongly corrupted observations that persist for a period of time. This situation is particularly critical for UWB multistatic radar applications in which we have blind zones corresponding to each pair of TX and RX antennas. It is well-known that particle filtering is powerful in blind zones due to the nonlinearity in state estimation. However, if we let particle filter estimate the velocity by extending the state space dimension and using the same weights for both position and velocity particles, consecutive deteriorations in velocity estimation cause moving the particles rapidly away from the true position and may lead to losing the track. Therefore, around the blind zones where the observations are poor for a considerable number of scan times, any strong clutter residue, a target maneuver or an extremely low signal-to-noise ratio can corrupt the velocity estimation and cause a divergence. The tracking may also diverge in distant areas from the TX antenna, because UWB signals are highly attenuated by distance. Although this divergence occurs rarely and most of the time the algorithm performs well, it is important to fix the issue and make the algorithm more stable. In our modified algorithm, we use particle filtering in a more controllable manner for estimating the velocity. As the dynamic model, we assume that the target average velocity is constant during a sliding window over time. Within each window, we give a weight to each estimated velocity according to its difference from the average velocity calculated in the previous scan time. The higher is the difference, the lower will be its contribution in calculating the mean. At the same time, we increase the process noise standard deviation proportional to this error to cover any potential maneuver. When the target is moving on a straight line and suddenly we observe that it deviates from its straight trajectory, there are two possibilities: either the target is still going on the straight line and we have corrupted observations or the observations are correct and the target has a maneuver. In order to cover both possibilities, we assume the first hypothesis, that is the target is still going on straight line and we have a wrong observation. So, we allow that estimation less affects the average velocity. On the other hand, we increase the process noise standard deviation to avoid losing the track if the second hypothesis was true
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(13) Here the state space is a 2 1 vector containing only the posi. tion components in and directions, that is, is a vector containing the mean of In the above equation, the movements for scan time calculated independently for and directions, is the process noise vector wherein each component is taken from a normal distribution with zero mean and standard deviation equal to the corresponding element of the vector . Again note that in this paper we denote the ’th . element of a generic vector by At each scan time, after estimating the position, we calculate the estimated movement as (14) If we denote the window size (as number of scan times) by , defined by the expectation then the mean of the movements of conditioned on the previous movement means in the current window, (15) can be calculated similar to estimated state in a particle filter with particles equal to , and the observations , . If we denote the weight , , the resulting of the particles by equation will be: (16) where (17) Here, is the error vector defined as . Now, we add more robustness to our algorithm for tracking high maneuvering targets. For this purpose, assume that the target is moving on a straight line, then we observe that it deviates at scan time . Therefore, according to (17) the estimated movement at scan time will have a low weight in calculation . Hence, is approximately equal to . However, if of the observed deviation at scan time is caused by a target maneuver, then the target movement at the next scan time will be approximately equal to its newly adopted movement . Therefore, we have to increase the process noise standard deviation
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V. SIMULATION RESULTS A square surveillance area of 100 100 meters is watched by a UWB radar sensor network composed of one transmitter and three receivers. Each TX and RX antenna is located at the middle of a square side. The origin of our assumed coordinate system is the lower left corner of the square. Therefore, the TX node is located at position (0,50), while the other 3 RX nodes are at positions (50,0), (100,50), and (50,100), respectively. Later, we will consider an example with more RX antennas. Algorithm 2 Calculate Movement Mean and Process Noise Standard Deviation 1: 2: 3: 4: if 5: for
Fig. 4. Flowchart of the modified tracking algorithm.
vector by to avoid losing the track at scan . In practice, an increment by a fraction of the error time is sufficient according to manoeuvrability of the target. Let’s denote this coefficient by . So, the process noise standard deviation vector at scan time is calculated by: (18) where is the process noise standard deviation in each dimenis the maximum sion for a non-maneuvering target and allowable process noise standard deviation in each direction to avoid that increases too much by large errors. The flowchart of the modified algorithm is depicted in Fig. 4. Pseudo-code descriptions for Initialize and Calculate Movement Mean and Process Noise Standard Deviation blocks are given by Algorithms 1 and 2, respectively. The blocks that are not described are the same as Fig. 3. For initialization, we assume that target positions at the first and second scan times are known by detection. Since we consider the initial particles as samples from a Gaussian distribution around the target position in the second scan time, having errors in detection can not affect the performance too much. Since in the modified algorithm we have removed the velocities from the state space, the algorithm complexity reduces much more than what it is added by simple required calculations for the movement means. Algorithm 1 Initialize 1: 2: 3: 4: 5: 6:
then do
6: 7:
end for
8: 9: else 10: for
do
11: 12:
end for
13: 14: end if 15: The TX node emits Gaussian monocycles with duration parameter 1.4 ns and whose power spectral density is assumed to exceed the Federal Communications Commission (FCC) mask by 10 dB. The number of pulses in each frame is and the frame duration is ms, resulting in a pulse interval ns. The sampling frequency is 1.5 GHz. For each RX node, the receiver noise figure and the antenna temperature are dB and K, respectively. These settings result in a transmitted signal power of 32.5 dBW and a received noise power 86.2 dBW. We consider a number of 100 pointwise objects to be present in the surveillance area as clutters. The clutters are distributed uniformly over the whole area. First, we consider static clutters with the same radar-cross-sections as that of the target. Later, we will consider moving clutters with different radar-cross-sections, drawn according to a Chi-squared distribution with two degrees of freedom (Swerling type I). Each RX node is assumed to implement a frame-to-frame clutter removal technique based on an IIR filter. In particular, we have considered a high-pass first-order filter with transfer function (hence with a pole equal to 0.9) which operates at a sampling frequency Hz.
SOBHANI et al.: TARGET TRACKING FOR UWB MULTISTATIC RADAR SENSOR NETWORKS
A single target with a radar-cross-section of 1 m is assumed to be present inside the area. The target is moving on a straight line starting from the origin of our coordinate system and with a constant velocity of 10 km/h, representing the speed of a human being walking quickly. Later, we will consider a more complicated trajectory. At each RX antenna, the received signal is constructed as the superposition of the direct path, clutter echoes, and ground reflection in addition to the target echo and the noise. The echo amplitudes have been simulated according to for the LOS path and for any object including the target [7], where and are the TX and RX antenna gains, respectively, which are both equal to 0 dB for our omnidirectional antennas and is the wave length which has been calculated based on the center frequency 4.5 GHz. Moreover, is the TX-RX distance, while and are the distances of the object from TX and from that RX, respectively. Finally, is the radar-cross-section of the object. In our numerical results, the system performance is measured in terms of both the CDF (Cumulative Distribution Function) and RMS (Root Mean Square) errors over 50 simulation runs, each with different noise and clutter realizations. For generating the RMS plot, we average the vector of estimation errors at all scan times over all simulation runs. For the CDF plot, we concatenate the estimation error vectors of all simulation runs and then we calculate the CDF for the resulting vector. Moreover, an example of a single simulation run showing the true and estimated target trajectories, antenna and clutter positions inside the area is shown for each scenario. For each scenario, we evaluate the performance of the particle algorithms described in Fig. 3 and Fig. 4. The performance of conventional Kalman filtering is shown for comparison. Tracking by Kalman filter requires the measured target positions as inputs. We have adopted the pixel-based approach used in [23] to estimate these values. For all tracking techniques, the corresponding parameters have been set to the values maximizing the performance. For the first particle algorithm has been set to 8 . For the modified particle algorithm we have set the window size to 20. Also, has been set to zero for all scenarios to show that even without increasing the process noise standard deviation according to errors, the algorithm performs well with both linear and complicated trajectories. Thus, the process noise standard deviation is always equal to in a range in both and directions; we have chosen between 0.04 m to 0.3 m based on the scenario. Note that in our simulations, we have considered a constant velocity (in amplitude) for the target over the whole trajectory. The role of is more important for higher maneuvers, for example when the target not only changes its direction but also introduces an acceleration. We have not considered such a scenario because of our particular surveillance application. Since the complexity of particle filtering increases with the number of particles, this value should be selected carefully. In Fig. 5, we have evaluated the effect of the number of particles on the tracking performance of both particle algorithms in terms of error CDF. The assumed trajectory is a straight line with slope 50 . We can see from the figure that above a cer-
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Fig. 5. The effect of number of particles on the tracking performance for static clutter and a straight line trajectory with a slope of 50 . (a): Particle algorithm. (b): Modified particle algorithm.
tain number of particles, the system accuracy improves very slowly. Thus, we set the number of particles equal to 200 for all our simulations, reaching a satisfying tradeoff between estimation accuracy and complexity. Furthermore, we can see that decreasing the number of particles has a lower impact on the performance of the modified particle algorithm compared to the first algorithm. In general, this would allow to use an even smaller number of particles, significantly reducing the computational complexity. However, we set this number to be 200 for both particle algorithms for comparison purposes. To evaluate the algorithms behavior over the area, we have simulated a straight line target trajectory with slope 50 , passing through different blind zones. Fig. 6 shows the corresponding results. In the subfigures representing the surveillance area, the triangle indicate the TX and the three RX antennas are represented by squares. The gray ellipses represent the blind zones. The small circles over the area represent the static clutters and the three large circles in the middle of three LOS lines show the ground reflection points. It can be seen from the figures that the system performance improves considerably when using particle filtering compared to Kalman filtering, particularly around the blind zones. As we can see from the figures, in these scenarios the performance of the modified particle algorithm slightly improves compared to the first particle algorithm.
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Fig. 6. Performance comparison of the particle algorithms vs. Kalman filter for static clutter and a straight line trajectory with a slope of 50 . (a): An example of surveillance area for particle algorithm. (b): An example of surveillance area for modified particle algorithm. (c): An example of surveillance area for Kalman filter. (d): CDF error plots. (e): RMS error plots.
Fig. 7. Performance comparison of the particle algorithms vs. Kalman filter for a static clutter and a maneuvering target. (a): An example of surveillance area for particle algorithm. (b): An example of surveillance area for modified particle algorithm. (c): An example of surveillance area for Kalman filter. (d): CDF error plots.
One of the advantages of particle filtering is in tracking targets with highly nonlinear trajectories. In Fig. 7 we have considered the case of a complex target trajectory. The target is moving
on the curve with constant velocity 10 km/h. In this trajectory, we have included various shapes such as wave-like curves, circle-like curves, small and sharp closed curves, straight lines,
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Fig. 8. Performance comparison of the particle algorithms vs. Kalman filter for dynamic clutter and a straight line trajectory with a slope of 50 . (a): An example of surveillance area for particle algorithm. (b): An example of surveillance area for modified particle algorithm. (c): An example of surveillance area for Kalman filter. (d): CDF error plots.
Fig. 9. Performance comparison of the particle algorithms for static clutter and a complicated trajectory with 6 RX antennas. (a): An example of surveillance area for particle algorithm. (b): An example of surveillance area for modified particle algorithm. (c): CDF error plots. (d): RMS error plots.
as well as sudden direction changes with various angles between 0 and 180 (in which the target suddenly reverses its direction).
It can be seen from the figure that the modified particle algorithm can track all maneuvers with high precision while Kalman
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Fig. 10. Performance comparison of the particle algorithms vs. Kalman filter for static clutter and a straight line trajectory with a slope of 50 with the power spectral density fitting the FCC mask. (a): An example of surveillance area for particle algorithm. (b): An example of surveillance area for modified particle algorithm. (c): An example of surveillance area for Kalman filter. (d): CDF error plots. (e): RMS error plots.
filtering exhibits large estimation errors. Although the first particle algorithm can track the curve with a good precision for most of the simulation runs (in this regard the example reported in Fig. 7(a) is meaningful), there are a few realizations for which the tracking diverges. This behavior can be seen from the algorithm error CDF plot. So far, the simulation results were for scenarios with static clutters having the same radar-cross-section as the target. Next, we consider dynamic clutters. Clutters are assumed to move with random velocities whose amplitudes and phases are drawn from uniform distributions over the ranges [0,1] km/h and , respectively. The radar-cross-section of the clutters are drawn from a Chi-squared distribution with two degrees of freedom (Swerling type I) at the beginning of a simulation and kept constant during that simulation. The echoes due to slowly moving clutters (low frequency components) are attenuated according to the filter frequency response. In contrast, the echo from the target, which is moving with a higher velocity, remains almost unaffected. Fig. 8 shows the corresponding plots. In this figure, the size of the circles is proportional to the clutter radar-cross-sections. The slow random movements of the clutters have also been represented in the figure through small clouds over the area. We note that Kalman filtering frequently fails, while the first particle algorithm performs well most of the times. However, as it can be seen from its corresponding CDF error plot, in a few simulations the algorithm diverges, mainly around the blind zones due to strong clutter residues.
Note that for all algorithms we have used a simple IIR filter as the clutter removal technique. A more complex processing can further reduce the amount of clutter residues and hence the number of divergences. In the modified particle algorithm, for dynamic clutters we have considered a directional process noise standard deviation in the direction of the estimated movement mean according to
(19)
This approach reduces the amount of clutter residues affecting the performance compared to the case in which the process noise standard deviation is equal to in both and directions. With this replacement, the modified particle algorithm always performs well in the moving clutters even with a simple IIR filtering as the clutter removal technique. Increasing the number of RX antennas provides more observations. Hence, it can help improve the tracking performance specially around the blind zones. To see that, we have considered six RX antennas located at positions (33,0), (66,0), (100,33), (100,66), (33,100) and (66,100), respectively. The assumed target trajectory is similar to the one in Fig. 7 and the clutters are static. The time settings have been changed slightly to ns and ms to include all possible echoes within a pulse interval. This scenario has been shown
SOBHANI et al.: TARGET TRACKING FOR UWB MULTISTATIC RADAR SENSOR NETWORKS
in Fig. 9. As we can see, the performance of both particle algorithms improves greatly with the number of receivers so that no divergence occurs even for the first particle algorithm. In all of the above scenarios, it is assumed that the transmitted power spectral density exceeds the FCC mask by 10 dB. In order to see the algorithms behavior in low signal-to-noise ratios, we have also considered a lower transmitted power spectral density fitting the FCC mask, that is, a transmitted signal power of 42.5 dBW, the received noise power being unchanged. Fig. 10 shows the results with static clutters. We see that Kalman filtering always fails while both particle filters still perform well. The modified particle algorithm slightly outperforms the first particle algorithm for this scenario. As it can be seen from the simulation results, the modified algorithm not only avoids track divergence in all scenarios, but also improves the estimation precision compared to the first particle algorithm. Another advantage of the modified particle algorithm is its high flexibility. Knowing some characteristics of the target can help improve the tracking performance even more by changing the parameter settings. For example, increasing the window size improves the tracking performance for linear trajectories while decreasing it improves the maneuvering ones. Similarly, increasing improves the tracking performance for maneuvering trajectories while decreasing it improves the linear ones. All the above advantages are achieved while the algorithm complexity is reduced significantly. As a final observation, we have measured the average simulation elapsed time for each data scan while the program was running on an Intel Core i5 CPU at 2.53 GHz with 4 GB RAM. For the first particle algorithm the result has been measured to be about 55 ms while for the modified particle algorithm it has been about 45 ms. Both amounts are less than the considered scan time duration (frame duration) which has been set to 68.3 ms. Thus, the real-time implementation feasibility is guaranteed. VI. CONCLUSION In this paper, a tracking algorithm based on particle filtering for UWB multistatic radars has been proposed. The particle weights have been derived assuming one transmitter and multiple receivers. Then, a modified version of the algorithm has been presented to solve some tracking problems, mainly caused by blind zones. It has been illustrated how the proposed algorithm can provide high estimation accuracy even at low signal-to-noise ratios in the presence of either static or dynamic clutter and how it can track even quite complicated manoeuvring target trajectories. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their insightful technical comments which helped to significantly improve this paper. REFERENCES [1] N. Patwari, J. Ash, S. Kyperountas, A. O. Hero, R. Moses, and N. Correal, “Locating the nodes: Cooperative localization in wireless sensor networks,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 54–69, Jul. 2005. [2] W. Headley, C. da Suva, and R. Buehrer, “Indoor location positioning of non-active objects using ultra-wideband radios,” in Proc. IEEE Radio Wireless Symp., Jan. 2007, pp. 105–108.
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[26] R. Herrmann, J. Sachs, M. Kmec, M. Grimm, and P. Rauschenbach, “Ultra-wideband sensor system for remote monitoring of vitality at home,” in Proc. 9th Eur. Radar Conf., Oct./Nov. 2012, pp. 234–237. [27] E. Piuzzi, S. Pisa, P. D’Atanasio, and A. Zambotti, “Radar cross section measurements of the human body for UWB radar applications,” in Proc. IEEE Int. Instrum. Meas. Technol. Conf., May 2012, pp. 1290–1293. [28] S. Blackman and R. Popoli, Design and Analysis of Modern Tracking Systems. Norwood, MA, USA: Artech House, 1999. Bita Sobhani received her M.Sc. Degree in Telecommunications Engineering in 2006, from Isfahan University of Technology (IUT), Iran. After her M.Sc., she worked as a researcher in Information and Communication Technology Institute and Foolad Technic International Engineering Company (FIECO), Isfahan, Iran. Since 2012 she has been a Ph.D. student at the Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi,” University of Bologna. Her research interests include Ultra-Wideband radar sensor networks, MIMO space-time coding, Zigbee mesh networks, automatic meter reading (AMR), industrial and building automation.
Enrico Paolini (M’08) received the Dr. Ing. degree (with honors) in Telecommunications Engineering in 2003 and the Ph.D. degree in Electrical Engineering in 2007, both from the University of Bologna, Italy. While working toward the Ph.D. degree, he was Visiting Research Scholar with the University of Hawai’i at Manoa. From 2007 to 2010, he held a postdoctoral position with the University of Bologna. Currently, he is an Assistant Professor at the Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi,” University of Bologna. His research interests include error-control coding, random access techniques, and radar sensor networks based on UWB. In the field of error correcting codes, has been involved since 2004 in several activities with the European Space Agency (ESA). He is a frequent visitor at the Institute of Communications and Navigation of the German Aerospace Center, where he was Visiting Scientist in the summer 2012 under a DLR-DAAD fellowship. Dr. Paolini is Editor for the IEEE COMMUNICATIONS LETTERS. He served on the Technical Program Committee at several IEEE International Conferences, and on the Organizing Committee (as treasurer) of the 2011 IEEE International Conference on Ultra-Wideband. He is member of the IEEE Communications Society and of the IEEE Information Theory Society.
Andrea Giorgetti (S’98–M’04–SM’13) received the Dr.Ing. degree (summa cum laude) in electronic engineering and the Ph.D. degree in electronic engineering and computer science, both from the University of Bologna, Italy, in 1999 and 2003, respectively. From 2003 to 2005, he was a Researcher with the National Research Council, and since 2006, he has been an Assistant Professor at the University of Bologna. During spring 2006, he was with the Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology (MIT), Cambridge, MA, USA. Since then he is a Research Affiliate of LIDS, MIT. His research interests include ultra-wide bandwidth communications systems, active and passive localization, wireless sensor networks, and cognitive radio.
Dr. Giorgetti is Technical Program Co-Chair of the Cognitive Radio and Networks Symposium at the IEEE International Conference on Communications (ICC), Budapest, Hungary, June 2013, and the Cognitive Radio and Networks Symposium at the IEEE Global Communications Conference (Globecom), Atlanta, GA, USA, December 2013. He was Technical Program Co-Chair of the Wireless Networking Symposium at the IEEE International Conference on Communications (ICC), Beijing, China, May 2008, and the MAC track at the IEEE Wireless Communications and Networking Conference (WCNC), Budapest, Hungary, April 2009. He is an Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS and for the IEEE COMMUNICATIONS LETTERS.
Matteo Mazzotti (M’08) received the Dr. Ing. degree (summa cum laude) in telecommunications engineering and the Ph.D. degree in electronic engineering, computer science and telecommunications from the University of Bologna in 2002 and 2007, respectively. He has worked with the National Research Council (CNR), Italy, and he collaborates with the National Inter-University Consortium for Telecommunications (CNIT), Italy. Currently, he is with the Center for Industrial Research on ICT (CIRI ICT) of the University of Bologna. He has participated in several national and international projects, such as the European projects Phoenix-FP6, Optimix-FP7 and Concerto-FP7. He serves as a reviewer for international journals and conferences and has participated in the organizing committees and technical program committees of several international conferences. His main research interests include wireless multimedia communications, joint source and channel coding, broadcasting technologies and UWB radio localization systems.
Marco Chiani (M’94–SM’02–F’11) received the Dr. Ing. degree (summa cum laude) in electronic engineering and the Ph.D. degree in electronic and computer engineering from the University of Bologna, Italy, in 1989 and 1993, respectively. He is a Full Professor in Telecommunications at the University of Bologna. During summer 2001, he was a Visiting Scientist at AT&T Research Laboratories, Middletown, NJ. Since 2003 he has been a frequent visitor at the Massachusetts Institute of Technology (MIT), Cambridge, where he presently holds a Research Affiliate appointment. He is leading the research unit of the University of Bologna on cognitive radio and UWB (European project EUWB), on Joint Source and Channel Coding for wireless video (European projects Phoenix-FP6, Optimix-FP7, Concerto-FP7), and is a consultant to the European Space Agency (ESA-ESOC) for the design and evaluation of error correcting codes based on LDPCC for space CCSDS applications. His research interests are in the areas of wireless systems and communications theory, including MIMO statistical analysis, codes on graphs, wireless multimedia, cognitive radio techniques, and ultra-wideband radios. He recently received the 2011 IEEE Communications Society Leonard G. Abraham Prize in the Field of Communications Systems, the 2012 IEEE Communications Society Fred W. Ellersick Prize, and the 2012 IEEE Communications Society Stephen O. Rice Prize in the Field of Communications Theory. He is the past chair (2002–2004) of the Radio Communications Committee of the IEEE Communication Society and past Editor of Wireless Communication (2000–2007) for the journal IEEE TRANSACTIONS ON COMMUNICATIONS. Since 2011 he has been a Fellow of the IEEE, named for “Contributions to wireless communication systems”. He is a Distinguished Lecturer for the IEEE ComSoc (2011/2012). In 2012 he has been appointed Distinguished Visiting Fellow of the Royal Academy of Engineering, UK.
